Some remarks concerning \(D^{*}\)-metric spaces
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Authors
Zead Mustafa
- Department of Mathematics, Statistics and Physics , Qatar University, Doha , Qatar.
M. M. M. Jaradat
- Department of Mathematics, Statistics and Physics , Qatar University, Doha , Qatar.
Abstract
In [S. Sedghi, N. Shobe, H. Y. Zhou, Fixed Point Theory Appl., {\bf 2007} (2007), 13 pages], Sedghi et al. introduced the notion of \(D^{*}\)-metric space and in [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik, \(\bf 64\) (2012), 258--266] the authors claimed that every \(G\)-metric space is \(D^{*}\)-metric. In this short paper we present examples to show that \(D^{*}\)-metric need not be \(G\)-metric as well as the \(G\)-metric need not be \(D^{*}\)-metric.
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ISRP Style
Zead Mustafa, M. M. M. Jaradat, Some remarks concerning \(D^{*}\)-metric spaces, Journal of Mathematics and Computer Science, 22 (2021), no. 2, 128--130
AMA Style
Mustafa Zead, Jaradat M. M. M., Some remarks concerning \(D^{*}\)-metric spaces. J Math Comput SCI-JM. (2021); 22(2):128--130
Chicago/Turabian Style
Mustafa, Zead, Jaradat, M. M. M.. "Some remarks concerning \(D^{*}\)-metric spaces." Journal of Mathematics and Computer Science, 22, no. 2 (2021): 128--130
Keywords
- Metric space
- \(D^{*}\)-metric space
- \(G\)-metric space
MSC
References
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[1]
M. M. M. Jaradat, Z. Mustafa, S. U. Khan, M. Arshad, J. Ahmad, Some fixed point results on $G$-metric and $G_b$-metric spaces, Demonstr. Math., 50 (2017), 190--207
-
[2]
S. U. Khan, J. Ahmad, M. Arshad, T. Rasham, Some new fixed point theorems in $C^*$-algebra valued $G_b$-metric spaces, J. Adv. Math. Stud., 12 (2019), 22--29
-
[3]
Z. Mustafa, Some new common fixed point theorems under strict contractive conditions in $G$-metric spaces, J. Appl. Math., 2012 (2012), 21 pages
-
[4]
Z. Mustafa, M. Arshad, S. U. Khan, J. Ahmad, M. M. M. Jaradat, Common fixed point for multivalued mappings in G-metric spaces with applications, J. Nonlinear Sci. Appl., 10 (2017), 2550--2564
-
[5]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289--297
-
[6]
S. Sedghi, N. Shobe, Common Fixed Point Theorems for two mappings in $D^{*}$-Metric Spaces, Math. Aeterna, 2 (2012), 89--100
-
[7]
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point in $S$-metric spaces, Mat. Vesnik, 64 (2012), 258--266
-
[8]
S. Sedghi, N. Shobe, H. Y. Zhou, A common fixed point theorem in $D^{*}$-metric spaces, Fixed Point Theory Appl., 2007 (2007), 13 pages